1) near nil radical
近似诣零根
1.
We show that the supersemiprime radical is e qual to the near nil radical which was defined by XIE Bang_jie in .
证明了超半素根与谢邦杰在 [2 ]中所定义的近似诣零根是相等
2) near nil semisimple ring
近似诣零半单环
3) nil radical
诣零根
1.
Those are strongly nil radical N S , quasi strongly nil radical N QS ,nil radical N ,quasi nil radical N Q and B nil radical N B (Baer module nil radical).
本文旨在系统阐述ＷｅａｋｅｒΓＮ－环的五个诣零根。
2.
This paper show: if M is a ring with the prime radiCal P(M), the socle Soc(M),the nil radical N(M) and the Levitzki nil radical L(M),then regarded as a Pring with P=M,Pp(M)=P(M),Socp(M)=Soc(M),Np(M)=N(M) and LP(M)=L(M).
证明了如果Ｍ是一个环，具有素根Ｐ（Ｍ），底座Ｓｏｃ（Ｍ），诣零根Ｎ（Ｍ）和Ｌｅｖｉｔｚｋｉ诣零根Ｌ（Ｍ），则Ｍ作为一个Γ－环（取Γ＝Ｍ）有：Ｐ（Ｍ）＝ＰΓ（Ｍ），Ｓｏｃ（Ｍ）＝ＳｏｃΓ（Ｍ），Ｎ（Ｍ）＝Ｎｒ（Ｍ）和Ｌ（Ｍ）＝ＬΓ（Ｍ
3.
In this paper, the definition of nil radical of zero normal NCD-ring R is given, and the proof is made for that nil radical n(R) is the greatest ideal of R and R / n(R)has no non-zero nil ideals when n(R) is the smallest ideal of R.
本文给出零正规ＮＣＤ－环Ｒ的诣零根ｎ（Ｒ）的定义，完成了“零正规ＮＣＤ－环Ｒ的诣零根ｎ（Ｒ）是Ｒ的最大理想及ｎ（Ｒ）是使商环Ｒ／ｎ（Ｒ）无非零诣零理想的最小理想”的证明。
4) Levitzki nil radical
Levitzki诣零根
5) B-nil radical
B-诣零根
1.
Because M/N is not necessarily strongly nil semi-simple, we then defined B-nil radical N_B, such that M/N_B is strongly nil semi-sinple, Finally, the sture theorem of strongly nil semi-simple weaker Γ_N-ring is proved.
本文定义了Weaker Γ_N-环,论证了在这个环M中必有强诣零根N,但M/N未必强诣零半单,故定义了B-诣零根N_B,M/N_B是强诣零半单的,最后给出了强诣零半单Weaker Γ_N-环的结构定理。
6) strongly nil radical
强诣零根
1.
The problem of existence of strongly nil radicalin in fed Γ-ring was solved byusing the theory of finit type in the theory of dynamical systems, and the stronger conclusion was obtained by induced the concept of strongly nil ideal of finit type.
利用符号动力系统中关于有限型子转移的若干深刻结果，得到结论：有限个元素的Γ－环－定存在强诣零根。
2.
In this paper, we defined the weaker Γ_N-ring, and proved that there exits a strongly nil radical N in any weaker Γ_N-ring M.
本文定义了Weaker Γ_N-环,论证了在这个环M中必有强诣零根N,但M/N未必强诣零半单,故定义了B-诣零根N_B,M/N_B是强诣零半单的,最后给出了强诣零半单Weaker Γ_N-环的结构定理。
补充资料：孤诣
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